You wouldn’t think that listening to former leaders of Israel’s secret service would put you in mind of a John Lennon song, but in “The Gatekeepers,” Dror Moreh’s fantastic documentary, it does.

That’s because, to a man, the six living former heads of Shin Bet, a secretive organization involved in every aspect of Israeli security and counterterrorism, sound a single refrain: All we are saying is give peace a chance.

They don’t use those words, of course. But it’s stunning nonetheless to hear these warriors talk about the failure of warfare, of violence, much of it conducted under their supervision, to solve the problems in the Middle East.

“I think, after retiring from this job, you become a bit of a leftist,” said Yaakov Peri, who was in charge of Shin Bet from 1988 to 1994.

It’s a remarkable evolution.

But “The Gatekeepers” is more than just six men talking. (None had ever spoken about his work before.) Using the interviews along with news footage and occasional re-enactments, Moreh conducts a kind of primer in the organization’s history, which is, in its own way, a history of modern Israel. It’s fascinating.

After the decisive victory in the Six-Day War in 1967, Shin Bet found itself without an enemy to fight, former director Avraham Shalom says. Although each man proves interesting in his own way, Shalom is the most complex. He favored a Palestinian state after the war. He also welcomed, after a fashion, the rise in terrorism that followed the fighting; it gave his organization a reason to exist once again.

Shalom would become controversial himself; in 1984 he ordered the killing of two Palestinians who hijacked a bus and had been captured alive. Although he at first is reluctant to talk about it, he says, eventually, that he did so because he didn’t want to see two more terrorists in court. Pressed about the morality of his decision, Shalom says, “In the war against terror, forget about morality.”

Chilling words, perhaps, coming from a kindly looking little old man who chuckles when he talks (although not when pressed). They make his later statements, that Israel should talk to everyone to seek an end to violence and that “we have become cruel,” all the more striking.

Each of the men has made decisions to have other men killed. They talk about the struggles, the difficulties, the justifications of those choices. If you have a chance to wipe out a kind of supergroup of terrorists meeting under the same roof but will almost certainly kill bystanders in the process, what do you do? There are debates over 1-ton bombs (that almost certainly will kill the innocent) and quarter-ton bombs that wind up not killing anybody, including the terrorists. This isn’t hypothetical. It really happened.

Terror also strikes within. The great failure of Shin Bet was its inability to prevent the assassination of Prime Minister Yitzhak Rabin, who signed the Oslo Accords outlining Palestinian self-government in 1993 and who was, the men insist, the only prime minister who gave Israel a real chance at peace. Carmi Gillon, the head of Shin Bet in 1995, when an extremist named Yigal Amir shot Rabin to death, talks about pleading with the prime minister to wear a bulletproof vest, to take greater precautions.

“He changed history,” Gillon says of Amir. “Big time.”

But the film isn’t just about history. It’s also about the future, which, the men say in various ways, looks bleak.

“You can’t make peace with military means,” former director Avi Dicther says. Ami Ayalon is even more blunt: Israel can “win every battle but lose the war.”

So why did these men speak? They never say, and Moreh doesn’t, either. Perhaps they feel guilty. Perhaps they’re trying to bring about a change in strategy or policy. Or perhaps they were just waiting for someone to ask them to.

Why they spoke up doesn’t really matter. It’s what they have to say that’s so important.

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